a position of this kind? On the one hand I understand him to reject it most decidedly. On the other hand, wherever anything like 'implication' or 'unity' is involved (and how much have we left where these are excluded?), Mr. Russell seems to myself to embrace a conclusion which in principle I find it hard to distinguish from my own. And, it being clear to me that there is something here which I have failed to comprehend, I must leave this fundamental issue and go on to consider some difficulties more in detail.
The notion of 'implication',1 I understand Mr. Russell to say, is necessary for mathematics; and let us consider very briefly what this notion involves. It seems to mean (if it means any thing) that something is both itself and more than itself. There is a difference here which is both affirmed and denied ; for of course that anything should imply merely itself is meaningless. But how can anything be at once itself and in any sense not-itself? Mr. Russell leaves us here, so far as I have seen, without any assistance. But with this we are face to face with the familiar problem of the one and many, the universal and particular. We are driven back to the immediate experience where the whole is in the parts and where, through the whole, the parts are in one another. But such an immediate experience seems in the first place (I would repeat) to contradict pluralism, and in the second place it offers by itself no theoretical solution. The same difficulty appears in 'such that'. If this phrase does not mean that a particular is also a universal, and with a certain conse quence, it surely has no meaning at all. But how to justify this necessary inconsistency Mr. Russell does not tell us. Among other fundamental troubles of the same kind I would mention the ideas of 'occupation' and of 'magnitude of'. Certainly Mr. Russell asserts here the existence of a relation, but this assertion to my mind seems obviously opposed to fact, and once more I find an unjustified recourse to the inconsistency of imme diate experience.
I will enter now on some instances of a somewhat different kind, where however the difficulty remains at bottom the same. I will not repeat what in a former chapter I have urged with regard
1 In connexion with 'implication' the axioms given by Mr. Russell (p. 16) demand the attention of logicians. But want of space makes it impossible for me to offer here any criticism.
